Surface approximation via sparse representation and parameterization optimization

• A new composite representation method is proposed for surface approximation.
• The results do not rely on basis functions with the parameterization optimization.
• Non-smooth features are fitted well even with smooth polynomial basis functions.
• An augmented Lagrange method based numerical algorithm is presented.

Surface approximation with smooth functions suffers the problems of choosing the basis functions and representing non-smooth features. In this work, we introduce a sparse representation for surfaces with a set of redundant basis functions, which efficiently overcomes the overfitting artifacts. Moreover, we propose an approach of parameterization transformation, which makes the possibility to represent non-smooth features by the composition of a smooth function and a non-smooth domain optimization. We couple the sparse representation and the parameterization transformation in a global optimization to respect sharp features with smooth polynomial basis functions. Our approach is capable for approximating a wide range of surfaces with different level of sharp features. Experimental results have shown the feasibility and applicability of our proposed method in various applications.

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